Answer to Question #148259 in Field Theory for Alfraid

Question

What is realtivsitic kinetic energy

Answer 1

The relativistic kinetic energy is given by

$E_{kinetic} = \frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}} - mc^2$

We see that it is a growing function of $v^2$ , is 0 for $v=0$ and goes to $+\infty$ when $v$ approaches $c$ . We can even show that for $v \ll c$ we have the classical expression of kinetic energy:

$E \underset{v/c\to 0}{\sim} mc^2 (1+\frac{1}{2}\frac{v^2}{c^2}) - mc^2 = \frac{mv^2}{2}$

The relativistic kinetic energy have the same physical meaning: it is the energy of an object related to it's movement independently of a direction.